As far as we know, activating the Ark and the Halo Array offered no sort of protection from the effects, so the Didact that activated it (Obviously Bornstellar since Ur-Didact hated the idea of the Halo Array) and would've been killed in doing so. The Ur-Didact, who we "kill" in Halo 4 would be most likely dead as well, though we all have our suspicions about whether or not he's gone.
I still question whether or not Bornstellar is actually gone though. It seems like the Librarian might still be alive, so I wouldn't be surprised to see either of the Didacts return (Bornstellar would be a most welcome ally
Fear not, my brothers! The next generation of gaming is upon us! Be glad! A reward for all your toil and all your sacrifices is upon us.
There are those who said this day would never come. What have they to say now?
(Yes, I ripped off a quote from Halo 2 and modified it to my own purposes. Sue me.)